1819.] Royal Academy of Sciences. 375 



the earth the motion which had been falsely attributed to the 

 sun, merited the appellation of being the founder of modern 

 astronomy. 



The Arabians preserved religiously the theories of the Greeks, 

 and made no change either in the form of their instruments, or 

 in the manner of using them ; but they had them much largef 

 and better divided ; the number of their observers was also much 

 greater ; and from the time of Almamoun, very apparent improve- 

 ments in respect to the elements of the theory of the sun, the 

 obliquity of the ecliptic, and the precession of the equinoxes, are 

 to be observed in their works. The introduction of sines and 

 versed sines by Albategnius ; of tangents by Aboul-Wesa ; of 

 subsidiary arcs to simplify a complex formula by Ebn-Jounis, 

 entirely changed the manner of making astronomical calcula- 

 tions. The Arabians also marked the times of phenomena with 

 more precision than the Greeks. Albategnius deduced from the 

 analemma a rule, in two parts, to find the altitude of a star by 

 the altitude of the pole, the declination, and the horary angle : 

 this is now the fundamental formula of modern trigonometry. 

 The same author then altered this formula by substituting the 

 versed sine for the cosine in order to find the hour by the altitude 

 of a star whose declination and right ascension are known. It 

 appears, however, that the Arabs made very little use of this 

 second rule, and that most commonly they found it sufficient to 

 determine the hour, after the manner of Hipparchus, by means 

 ■of ■an astrolabe, or planisphere, which served at the same 

 time to observe the altitude, and to dispense with a trigonome- 

 trical calculation. It was shown in the Ancient Astronomy that 

 Hipparchus invented this instrument to find the hour of the night 

 by means of a star ; of course he could find the hour of the day 

 much easier by the sun. 



The Arabians, in adopting the Greek astronomy, were not less 

 careful in collecting the astrological reveries of the Chaldeans : 

 they applied their trigonometry to them, and invented new 

 methods of dividing the heavens into 12 houses. These methods, 

 brought to perfection by Regiomontanus, and especially by 

 Magini, are translated into modern formula?, and the whole of 

 them applied to the calculation of the same nativity ; so that a 

 judgment may be formed of their differences, and of the uncer- 

 tainties which they must add to those predictions, of which the 

 fundamental principles are, in other respects, a mass of purely 

 arbitrary suppositions, the fruits of credulity, or rather of charla- 

 tanism. 



Dialling, which is at present considered only as a curious 

 application of astronomy, constituted at that time an integral 

 part of it, from the commodiousness of good sun-dials in exhibit- 

 ing the civil hours, and in regulating clepsydras. Without 

 changing in the least the theory of the Greeks, the Arabs, 

 studying the analemma of Ptolemy, found means to derive from 



